Electronic Communications in Probability

Concavity of entropy along binomial convolutions

Erwan Hillion

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Motivated by a generalization of Sturm-Lott-Villani theory to discrete spaces and by a conjecture stated by Shepp and Olkin about the entropy of sums of Bernoulli random variables, we prove the concavity in $t$ of the entropy of the convolution of a probability measure $a$, which has the law of a sum of independent Bernoulli variables, by the binomial measure of parameters $n\geq 1$ and $t$.

Article information

Electron. Commun. Probab., Volume 17 (2012), paper no. 4, 9 pp.

Accepted: 6 January 2012
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 94A17: Measures of information, entropy

Olkin-Shepp conjecture concavity of entropy binomial distribution

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Hillion, Erwan. Concavity of entropy along binomial convolutions. Electron. Commun. Probab. 17 (2012), paper no. 4, 9 pp. doi:10.1214/ECP.v17-1707. https://projecteuclid.org/euclid.ecp/1465263137

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